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A new method for optimal sensor placement based on variable importance of machine learned models is proposed. With its simplicity, adaptivity, and low computational cost, the method offers many advantages over existing approaches. The new…
Pressure field estimation from PIV data has been a well-established technique. However, time-resolved pressure estimation strongly depends on the temporal resolution of the PIV measurements. Generally, PIV data has limited time resolution…
Four different applications of spectral proper orthogonal decomposition (SPOD): low-rank reconstruction, denoising, frequency-time analysis, and prewhitening are demonstrated on large-eddy simulation data of a turbulent jet. SPOD-based…
We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic…
An adaptive algorithm for spectral proper orthogonal decomposition (SPOD) of mixed broadband-tonal turbulent flows is developed. Sharp peak resolution at tonal frequencies is achieved by locally minimizing the bias of the spectrum. Smooth…
While proper orthogonal decomposition (POD) is widely used for model reduction, its standard form does not take into account any parametric model structure. Extensions to POD have been proposed to address this, but these either require…
In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…
Depth maps captured by modern depth cameras such as Kinect and Time-of-Flight (ToF) are usually contaminated by missing data, noises and suffer from being of low resolution. In this paper, we present a robust method for high-quality…
We investigate the sensitivity of reduced order models (ROMs) to training data resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive…
We consider a shape optimization based method for finding the best interpolation data in the compression of images with noise. The aim is to reconstruct missing regions by means of minimizing a data fitting term in an $L^p$-norm between…
A quantitative evaluation method for a reduced-order model of the flow field around an NACA0015 airfoil based on particle image velocimetry (PIV) data is proposed in the present paper. The velocity field data obtained by the time-resolved…
This paper presents three new computational methods for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to random input. The first method represents a novel integration of…
Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…
A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…
The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, for model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by…
This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming,…
The sparse pseudo-input Gaussian process (SPGP) is a new approximation method for speeding up GP regression in the case of a large number of data points N. The approximation is controlled by the gradient optimization of a small set of M…
Diffusion-based inpainting can reconstruct missing image areas with high quality from sparse data, provided that their location and their values are well optimised. This is particularly useful for applications such as image compression,…
We consider the frequency domain form of proper orthogonal decomposition (POD) called spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space-time POD problem for statistically stationary flows and leads to…
Engineering simulations are usually based on complex, grid-based, or mesh-free methods for solving partial differential equations. The results of these methods cover large fields of physical quantities at very many discrete spatial…